Energy harvesting (also known as power harvesting or energy scavenging) is a process by which energy is derived from external sources (e.g., solar power, thermal energy, wind energy, salinity gradients, and kinetic energy), captured, and stored for small, wireless autonomous devices, like those used in wearable electronics and wireless sensor networks. For example, piezoelectric transducers are employed for harvesting electrical power from vibrations. Different AC-DC converters are described in the literature in order to rectify the AC power and extract the maximum amount of energy.
Possible applications of energy harvesters comprising such AC-DC converters for piezoelectric generators are, e.g., in applications like highway bridges (structural health monitoring) or railway trains (tracking and tracing). The frequency range of the vibrations associated to these applications is between 2 and 20 Hz, whereas mean accelerations are around 0.1 g.
When a piezoelectric material is mechanically excited, it transforms the mechanical energy into electrical energy. The AC power available between its electrical terminals has to be rectified to obtain DC power. A control circuit allows switching the transistors of a non-linear rectifier technique (SSHI) that provides better results than a diode bridge rectifier.
When a piezoelectric element is in open circuit, the derivative of its voltage and the derivative of its displacement are proportional since I=0.I=αdu/dt−C0dv1/dt, 
where I is the current flowing out of the piezoelectric element, u is the piezoelectric displacement, v1 is the piezoelectric voltage, a is the force factor and C0 is the capacitance of the piezoelectric element (cf. S. Priya and D. J. Inman, Energy Harvesting Technologies, Springer, 2009, pp. 209-259).
There are two SSHI techniques: parallel and series. In the series SSHI circuit shown in FIG. 1, the inductor and the switch are connected in series between the piezoelectric element and the diode bridge and the filter capacitor. In the case of the parallel SSHI technique shown in FIG. 2, the switch and the inductor are connected in parallel to the piezoelectric element and the diode bridge and the filter capacitor are connected afterwards.
The series SSHI converter (FIG. 1A) remains in open circuit almost all the time and the switch that connects the piezoelectric element to the inductor, the diode bridge and the load is closed just for a short time. For this converter, it can be considered that when there is a piezoelectric voltage peak, there is also a peak displacement of the piezoelectric element. In this way, the power harvested from the piezoelectric element is maximum. Therefore, a voltage peak detector circuit is the appropriate control circuit for the series SSHI converter in order to maximize the harvested power.
For the parallel SSHI converter, (FIG. 2A), the piezoelectric element is continuously connected to the rectifier bridge and the output load which creates a phase shift between the derivatives of the displacement and the voltage of the piezoelectric element, and therefore a peak voltage detector circuit cannot detect the peak displacement without error.
A voltage peak detector circuit is one of several typically employed control circuit for switching the transistors of the SSHI converters.
The AC power delivered by piezoelectric transducers is usually rectified employing a diode bridge and a filtering capacitor. Recently, an AC-DC converter which employs an inductor connected through a switch to the piezoelectric element has been proposed. The switch is closed when the piezoelectric voltage peak is reached. In this moment, the connection of the piezoelectric element with the inductor causes a resonant effect and a fast inversion of the piezoelectric voltage. After the piezoelectric voltage inversion, the switch is opened until a new peak is detected.
Commonly used control circuits for the switching transistors of the SSHI circuits use the piezoelectric voltage as input signal. These control circuits employ a peak detector and a comparator for generating the gate signal. The peak detector changes its polarity when the piezoelectric voltage has reached a peak and the comparator provides the positive and negative voltage levels for switching the transistors.
The implementation of the self-powered control circuit is done in the literature employing primarily two different circuits. FIG. 3 shows a solution for detecting positive peaks which is described by M. Lallart and D. Guyomar in “An optimized self-powered switching circuit for non-linear energy harvesting with low voltage output,” Smart Materials and Structures, Vol. 17, No. 3, 2008 and also in an international patent application PCT/FR2005/003000 (publication number: W0/2007/063194) by C. Richard, D. Guyomar and E. Lefeuvre entitled “Self-powered electronic breaker with automatic switching by detecting maxima or minima of potential difference between its power electrodes”. The peak detector circuit is composed by resistor R3, diode D3 and capacitor C. The direction of the diode assures that only positive peaks are detected. This peak detector circuit is a differentiator. When the voltage on the emitter of transistor T2 is higher than the voltage on the base, transistor T2 starts conducting and diode D3 is reverse biased since the voltage on the capacitor is bigger than the piezoelectric voltage. Since the base voltage of transistor T1 is higher than its emitter voltage, transistor T1 starts conducting and capacitor C is discharged. A complementary control circuit with a switch is used for detecting the negative peaks of the piezoelectric element.
Another solution available in the literature consists of a passive differentiator with hysteresis and a discrete comparator (see FIG. 4) which is described in S. Ben-Yaakov and N. Krihely, “Resonant rectifier for piezoelectric sources”, Applied Power Electronics Conference and Exposition, 2005, APEC 2005, Twentieth Annual IEEE, vol. 1, pp. 249-253, 6-10 Mar. 2005. The passive differentiator detects when there is a voltage peak changing the polarity of its output. The output of the passive differentiator is connected to the negative input of the comparator whereas the positive input is connected to the piezoelectric reference terminal. The output of the comparator is connected to the gate of the transistors for switching them appropriately. The authors claim that the differentiator with hysteresis prevents undesired triggers through Rhys. The transfer function of a differentiator composed by a capacitor Cder and a resistor Rder is:
            V      out              V      in        =      s          s      +              1                              R            der                    ⁢                      C            der                              
If a resistor Rhys is connected in parallel to capacitor Cder, the transfer function of this circuit is given by:
            V      out              V      in        =            s      +              1                              R            hys                    ⁢                      C            der                                      s      +                                    R            der                    +                      R            hys                                                R            der                    ⁢                      R            hys                    ⁢                      C            der                              
This transfer function has a zero located at ωz=1/(RhysCder) and a pole located at ωp=(Rder+Rhys)/(RderRhysCder). For a proper operation of the circuit as a differentiator, ωz is smaller than ωp. This circuit will act as a differentiator for angular frequencies which fulfill that 10ωz<ω<0.1ωp.
The previous solution employs the same control circuit for detecting positive and negative voltage peaks.
The piezoelectric equivalent circuit at a given resonant frequency can be represented by an internal sinusoidal current source and a capacitor in parallel (in S. Ben-Yaakov and N. Krihely, “Resonant rectifier for piezoelectric sources”, Applied Power Electronics Conference and Exposition, 2005, APEC 2005, Twentieth Annual IEEE, vol. 1, pp. 249-253, 6-10 Mar. 2005). The current source of the model is proportional to the velocity of the piezoelectric element, and therefore proportional to the derivative of the piezoelectric displacement. Hence, when there is a zero crossing of the sinusoidal current source, the optimum point for maximizing the harvested piezoelectric power takes place.
If the piezoelectric voltage inversion takes place at the peak displacement, like it occurs in the series SSHI converter, piezoelectric voltage V(vpiezo+)−V(vpiezo−) and internal current source I(V1) have the same polarity and the power harvested by the piezoelectric element is maximum (see FIGS. 5A and 5B). However, since the piezoelectric element typically is not in open circuit in the parallel SSHI converter, the piezoelectric peak voltage typically does not correspond at all with the peak displacement.
If the piezoelectric voltage inversion does not take place when there is a peak displacement, there are two possibilities: the piezoelectric voltage inversion has taken place before or after the peak displacement.
If the piezoelectric voltage inversion is done after the peak displacement, there is a time period before the piezoelectric voltage inversion where the piezoelectric voltage and current do not have the same polarity, and therefore the power harvested by the piezoelectric element is not maximum. However, the state-of-the-art peak detectors do not produce false peak detection under this circumstance. FIGS. 6A and 6B show a simulation example where the piezoelectric voltage inversion takes place after the peak displacement.
If the piezoelectric voltage inversion is done before the peak displacement, it means that the internal piezoelectric current source has the opposite polarity of the piezoelectric voltage and as long as this situation takes place, the internal capacitor of the piezoelectric element is discharged. This circumstance induces at the piezoelectric voltage waveform a local maximum and minimum that the state-of-the art differentiators detect sometimes as peaks. FIGS. 7A and 7B present a simulation that illustrates the scenario with local maximum and minimum after the piezoelectric voltage is inverted where there is no false detection of the piezoelectric voltage peaks, while FIG. 8 presents a simulation that illustrates the same scenario but with false detection of the piezoelectric voltage peaks. The false detection of the piezoelectric voltage causes a reduction of the harvested power. Then, a peak detector that rejects this false detections is of special interest for implementing the control of the parallel and the modified parallel SSHI converters.
When the piezoelectric voltage inverses its polarity, an overshoot may occur, which may be caused by the discharge of the internal piezoelectric capacitor when the internal current source has a different polarity than the piezoelectric voltage. The overshoot is a local maximum or minimum so that commonly used peak detectors may indicate the occurrence of a peak due to the overshoot. However, such a local maximum/minimum caused by such an overshoot immediately following a commutation of the piezoelectric voltage is typically not significant for an upcoming switching event to be performed by the switch. Therefore, a detection of such an overshoot as a switching-event-relevant peak is a false detection which is prone to disturb the operation of the SSHI AC/DC converter, thereby possibly reducing the harvested power.